#Measurement #Year11 #Standard >[!info]- [Applications of measurement | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n11/fad74ae493) >- MST-11-05 solves problems involving measurement in practical contexts ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ---------------------------- | ------------------------------------------------------ | ----------------------------------------------- | | [[Length]] | - perimeter of plane shapes | - *repeated content* | | [[Right-angled Triangles]] | - Pythagoras' theorem | - *repeated content*<br>- irregular shaped land | | [[Area]] | - converting units of area<br>- area of plane shapes | - *repeated content*<br>- trapezoidal rule | | [[Area and Surface Area A]] | - surface area of prisms, cylinders. | - *repeated content* | | [[Area and Surface Area B]] | - surface area of spheres, composite solids<br> | - *repeated content* | | [[Volume A]] | - surface area of prisms and composite solids | - *repeated content* | | [[Volume B]] | - volume of pyramids, cones, spheres, composite solids | - *repeated content* | | [[Numbers of Any Magnitude]] | - converting metric units, significant figures | - *repeated content* | ## Practicalities of measurement - Identify and convert between the metric units of length: millimetres (mm), centimetres (c), metres (m) and kilometres (km) - Identify and convert between metric units of area using $1\ \text{cm}^2\ =100\ \text{mm}^2$, $1\ \text{m}^2\ =10\ 000\ \text{cm}^2$, $1\ \text{ha}\ =10\ 000\ \text{m}^2$, and $1\ \text{km}^2\ =1\ 000\ 000\ \text{m}^2$ - Identify and convert between metric units of volume, using $1 \text{ cm}^{3}=1000\text{ mm}^3$, $1 \text{ m}^{3}=1\ 000\ 000\text{ cm}^3$, and $1 \text{ km}^{3}=1\ 000\ 000\ 000\text{ m}^3$ - Identify and convert between the metric units of capacity: millilitres (mL), litres (L), kilolitres (kL) and megalitres (ML) - Identify and between metric units of volume and capacity, using $1\ \text{cm}^3\ =1000\ \text{mm}^3$, $1\ \text{cm}^3\ =1\ \text{mL}$, $1\ \text{m}^3\ =1000\ \text{L}=1\ \text{kL}$, $1\ 000\ \text{kL}\ =1\ \text{ML}$ - Identify and convert between the metric units of mass: milligrams (mg), grams (g), kilograms (kg) and tonnes (t) - Apply scientific notation to represent numbers involving standard prefixes: nano- (n) for ${10}^{-9}$, micro- (µ) for $10^{-6}$, milli- (m) for $10^{-3}$, centi- (c) for ${10}^{-2}$, kilo- (k) for ${10}^3$, mega- (M) for ${10}^6$, giga- (G) for ${10}^9$ and tera- (T) for ${10}^{12}$, with and without a required number of significant figures ## Perimeter, area, and volume - Solve practical problems requiring the calculation of perimeters and areas of triangles, rectangles, parallelograms, trapeziums, circles, sectors of circles and composite shapes in a variety of contexts - Apply Pythagoras’ theorem to solve problems involving right-angled triangles - Calculate perimeters and areas of irregularly shaped blocks of land by dissection into triangles, rectangles and trapeziums - Solve practical problems involving the surface area of prisms, cylinders, spheres and composite solids in a variety of contexts - Solve practical problems involving volume and capacity of prisms, cylinders, spheres, cones, pyramids and composite solids in a variety of contexts - Apply the Trapezoidal rule $A\approx\frac{h}{2}\left(d_f+d_l\right)$, where $A$ is the area, $d_f$ and $d_l$ are the lengths of the parallel sides of the trapezium, $d_f$ is the first length and $d_l$ is the last length, and $h$ is the perpendicular distance between them, to solve a variety of practical problems involving area, volume and capacity for up to four applications